Incomplete Generalized (p, q, r)-Tribonacci Polynomials

Shattuck M., TAN E.

APPLICATIONS AND APPLIED MATHEMATICS-AN INTERNATIONAL JOURNAL, cilt.13, sa.1, ss.1-18, 2018 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 1
  • Basım Tarihi: 2018
  • Dergi Adı: APPLICATIONS AND APPLIED MATHEMATICS-AN INTERNATIONAL JOURNAL
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.1-18
  • Anahtar Kelimeler: Tribonacci polynomials, Incomplete tribonacci numbers, Polynomial generalization, Generating function, Combinatorial identity, Fibonacci polynomials, Riordan array, SCHRODER MATRIX, FIBONACCI
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper, we consider an extension of the tribonacci polynomial, which we will refer to as the generalized (p, q, r)-tribonacci polynomial, denoted by T-n,T-m (x). We find an explicit formula for T-n,(m) (x), which we use to introduce the incomplete generalized (p, q, r) -tribonacci polynomials and derive several properties. An explicit formula for the generating function of the incomplete generalized polynomials is determined and a combinatorial interpretation is provided yielding further identities.